Misner-Thorne-Wheeler, p.92, Box 4.1, typo?

In Misner-Thorne-Wheeler Gravitation, Chapter 4, Page 92, Box 4.1, at section 4, there is a formula for the contraction of a p-form and a p-vector. Now, it states that the contraction of a p-form basis with a p-vector basis gives the antisymmetrizer symbol, [tex]\left\langle {\omega ^{i_1 } \wedge \ldots \wedge \omega ^{i_p } ,e_{j_1 } \wedge \ldots \wedge e_{j_p } } \right\rangle = \delta ^{i_1 \ldots i_p } _{j_1 \ldots j_p } [/tex] and there is a reference to exercises 3.13 and 4.12. I tried this part many many times and I always find the result to be p! times the antisymmetrizer. I also compared it for the case p=2 using the definition of the symbol from exercise 3.13, still the same result, I get an overall 2. Can anybody please explain what am I doing wrong here?

No typo. The symbol [tex]\delta^{ij}_{kl}\equiv \delta^{[i}_{k}\delta^{j]}_{l}\equiv \frac{1}{2!}\left(\delta^{i}_{k}\delta^{j}_{l}-\delta^{j}_{k}\delta^{i}_{l}\right)[/tex] (which generalizes to n indices with a 1/n! factor), and basis 1-forms act on basis vectors as [tex]\omega^{i}(e_{j})=\delta^{i}_{j}[/tex].